To solve the expression 5 + 3 × 5 ÷ 8, first apply the order of operations (PEMDAS): multiply 3 × 5 = 15, then divide 15 ÷ 8 = 15/8, and finally add 5 + 15/8. To add fractions with different denominators, use the butterfly method: multiply cross terms (5 × 8 = 40 and 1 × 15 = 15), add these products (40 + 15 = 55) for the new numerator, and multiply the denominators (1 × 8 = 8) for the new denominator, resulting in 55/8. Converting to decimal form through long division yields 6.875, and as a mixed number, it is 6 7/8.
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Why 6th Grade Math Tricks Most Adults? (5 + 3 × 5 ÷ 8)Hinzugefügt:
Hi everyone. Pamas is going to help us solve this tricky math problem. Pamas is saying that 3 * 5 goes first. So what is 3 * 5? 15. Good job. So I'll write five + 15 / 8. Next, Pandas is saying, "Hey, 15 / 8 goes first." So, what is 15 / 8? H, I don't know. So, I'm going to write it in a fraction form to make the math fun and easy. 15 over 8. And let's bring the 5 plus down. That is a plus sign there.
So, I'll bring the five down, but in a fraction form to make the math fun and easy. 5 over 1 = 5 does not change the five plus 15 over 8. Notice that yes, we're adding two fractions, but the denominators are different. So, we're going to use the butterfly method. So, I will draw two wings, two antennas, and a body.
So, here's the first wing.
5 * 8. You're not adding, you're multiplying what's inside the wing. And here's the antenna.
So, what is 5 * 8? 40. Good job. Next, we draw the other wing.
And what is 1* 15?
15. Good job. So, I'll write 15 here.
Lastly, uh what is 1* 8? This is the body. 1* 8 = 8. And don't leave yet because we need to figure out the decimal answer. Maybe the answer is 7.5 or it could be 712, but we don't know that. And if you have not subscribed to the channel, please subscribe to the channel to support. And if you subscribe, thank you so much for subscribing and supporting. And let's continue solving solving this math problem. So the denominator is going to be 8 and the numerator is adding 40 + 15. So 40 + 15 is 55.
So I'll write 55 as our new numerator.
and 55 over 8 cannot be broken down further. So this is your answer in a improper fraction form. Now let's go ahead and figure out the decimal answer and the mixed number answer to this math problem using long division. So we have an answer of 5 over 8, right? And then I'll write the mixed number answer here and then the decimal answer here using long division.
So the 55 goes inside the long division symbol. This is called the dividend. And the eight goes outside the long division symbol. That is called the divisor. So how many times can 8 fit into 55? H.
Well, I know that 8 * 5 is 40. So, we're getting close to 55.
8 * 6 is 48. I just added another eight.
So, 48. We're almost close to 55.
8 * 7 is 56. So, we went one over 55. So six is the number we'll add here. So that's what I'll do. So I'll write six here. And then I'll I'll I'll change the color. So it'll be six.
And then we multiply 6 * 8 which is 48.
And then let me use a different marker, a thinner marker. So we can do some subtraction here. So we need to the five needs to borrow. So this becomes four.
This becomes 15. So 15 drop 8 5 6 7. So it's seven. 55 - 48 is seven. Oops.
Dropping stuff. Sorry. Next. Let me erase all this for space.
And we know that um we have we we know that eight cannot fit into seven. So seven needs to borrow a zero. So we're going to add a decimal after the 55 and a decimal after the six and we write a zero here. We bring down the zero, give it to the seven, and the seven becomes 70. So how many times can eight fit into 70? Sorry, I erased the multiplication here. So, we had 8 * um 7, which equals oops, let me write this a little bit to the other side here. 8 * 7.
So 8 * 7 is 56 and 8 * 8 is 64. So, we're getting close to 70. 8 * 9 is the hand trick. So drop the the eighth number 72 72. So that goes 2 over 70. So we are going to use this eight and write it here because 64 is the closest we'll get to 70. If we use nine that goes over 70 uh so it goes it's hard it goes 2 over 70. So we stick to the 8. And then 8 * 8 is 64.
And then 70 - 64 is six.
So I'll write six, right? And then how many times can 8 fit into six?
Well, the six needs to borrow a zero. So we write a zero there. We bring it down.
Give it to the six. Now the six becomes 60. So, how many times can 8 fit into 60? Well, I know that 8 * 8 = 64. So, that goes over four.
So, it must be 8 * 7 which equals 56.
So, we'll write 56 here and then write the seven. That seven is is coming from that 7 and 7 * 8 is 56. And then 60 minus 56 is 4. And then how many times can 8 fit into four? You cannot. So the four needs to borrow a zero. So we give a zero to the four and the four becomes 40. How many times can 8 fit into 40?
Well, we know 8 * 5 is 40. So it's 5. 5 * 8 is 40 and 40 - 40 is zero. So your decimal answer is 6.875 and the mixed number is using this whole number the six and then the remainder which is seven goes on top of the fraction bar and the eight goes below the fraction bar. And there you go. And if you want to go back to uh the improper fraction, all you have to do is multiply six time 6 * 8 or 8 * 6. 8. 8 * 6 is 48.
So 48 + 7 gives you 55. And then you keep the denominator the same. So you'll have 55 over 8. So that's all you have to do. And there you go. If you have not subscribed to the channel, please subscribe to the channel to support.
Thank you so much for watching and please give this video a like and I'll see you in the next video. Bye.
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